Question

$\Delta = \left| \begin{matrix} a & a + b & a + b + c \\ 3a & 4a + 3b & 5a + 4b + 3c \\ 6a & 9a + 6b & 11a + 9b + 6c \end{matrix} \right|$where$a = i,b = \omega,c = \omega^{2}$, then $\Delta$is equal to.

• A. I
• B. $- \omega^{2}$
• C. $\omega$
• D. $- i$

Answer 1

Answer: (A)

I

Answer 2

We first operating $R_{3} - 2R_{2}$ and $R_{2} - 3R_{1}$ in given determinant, then we get $= a\lbrack a^{2} + ab - 2a^{2} - ab\rbrack = - a^{3} = i$.